Quadrilaterals

A quadrilateral is a four sided polygon. Probably the shape most people think of when thinking about a quadrilateral is a square but there are other shapes that fit into this category as well such as a rectangle, a rhombus, a trapezoid, and a parallelogram. Can a quadrilateral have two (or more) classifications? Let's say your friend Sally McKnowitall told you that a square is a rectangle. Would you believe her? In order to figure that out we must first look at the characteristics of each type of quadrilateral. Below is an example of a sheet you can pass out to your students to have them fill out.

To see if Sally is right or not let's compare a square's characteristics with a rectangle's characteristics.

Square

• 4 equal sides
• Opposite sides are parallel
• 4 right angles

Rectangle

• 4 sides
• 4 right angles
• Pairs of opposite sides are equal
• Opposite sides are parallel

As you can see, a square has 4 equal sides. A rectangle has four sides and opposite sides are equal. A square has opposite sides that are equal, they just happen to be the exact same size as the other pair so technically that characteristic of a square does fit into the rectangle classification as well. Both the square and the rectangle have to have right angles and have to have opposite sides that are parallel to each other so a check goes in both those boxes as well. So, your friend Sally McKnowitall was correct - a square IS a rectangle as well. However, the only rectangle that is also a square would be a rectangle that has four equal sides since if the sides are not all the same length it does not classify as a square.

Now let's look at the characteristics for a rhombus.

Rhombus

• 4 sides
• 4 equal sides
• opposite sides are parallel

A rectangle can not also be classified as a rhombus unless the rectangle has 4 equal sides. Most rectangles would not fall into this category since most rectangles have parallel sides of different lengths. A square could however be classified as a rhombus as well. A square has four equal sides and opposite sides are parallel. A square just happens to have 4 right angles as well so therefore, the only rhombus that could be classified as a square also is a rhombus with 4 right angles as well. 

Now let's look at the characteristics for a parallelogram.

Parallelogram

• 4 sides
• Pairs of opposite sides are parallel
• Opposite sides are equal

A rectangle, a square, and a rhombus all have opposite sides that are parallel. They all also have opposite sides that are equal so all three can also be classified as a parallelogram as well. 

Lastly, let's look at the characteristics for a trapezoid.

Trapeziod

• 4 sides
• one pair of unequal parallel sides

Since a square, a rectangle, a rhombus, and a parallelogram all need to have opposite sides that are equal, none of them can also be classified as a trapezoid. The only thing that can be a trapezoid is a trapezoid and a trapezoid can not be classified as anything other than a trapezoid. 

I hope this helped you learn quadrilaterals. Having your students fill out the sheet really helps them to understand the material better because having a list like that all in one spot makes it easy to compare characteristics. You could also have your students fill out a quadrilateral family tree like this to help them understand the relationships better. Happy teaching! 😄